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JEE Main Math Class 12 Limits and Derivatives Part 1 Questions
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© examsnet.com
Question : 3
Total: 100
If
lim
n
→
∞
(
n
+
1
)
k
−
1
n
k
+
1
[
(
n
k
+
1
)
+
(
n
k
+
2
)
+
.
.
.
+
(
n
k
+
n
)
]
, then the integral value of
k
is
=
33
⋅
lim
n
→
∞
1
n
k
+
1
⋅
[
1
k
+
2
k
+
3
k
+
.
.
.
+
n
k
]
equal to
[25-Jul-2022-Shift-1]
Your Answer:
Validate
Solution:
lim
n
→
∞
(
n
+
1
n
)
k
−
1
1
n
∑
r
=
1
n
(
k
+
r
n
)
=
33
lim
n
→
∞
1
n
∑
k
=
1
n
(
r
n
)
k
⇒
∫
0
1
(
k
+
x
)
d
x
=
33
∫
0
1
x
k
d
x
⇒
2
k
+
1
2
=
33
k
+
1
⇒
k
=
5
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